How to run some code repeatedly after an interval that can changes?

I'm using a thread in JavaFX to repeat my code after an interval (initially 1s), but I want to be able change the interval that the thread is using to 500ms or 333ms based on user choice (I have a button in a menu bar to change for each choice). I did tried things like shutDown() if the user clicks on one of the buttons and initiate it again with the new value, but didn't work. Any ideas?

Here's the relevant part of my code:

ScheduledExecutorService exec = Executors.newSingleThreadScheduledExecutor();
exec.scheduleAtFixedRate(() -> {
//refresh users, line and "guiche"
updateFila(usuarios, guiches, fila);
updateGuiche(guiches, fila, graphicsContext);
turno++;
//ends the code after the end of the line
if (done) {
exec.shutdown();
}
}, 0, 1000, TimeUnit.MILLISECONDS); //This is interval that I need to change after user choice

I know that I'm executing scheduleAtFixedRate() right now, but it was just to see if the logic was fine.

Additionally, I need to pause, resume and reset the thread, all based on user click.